Antiferroelectric liquid crystal layers

The chapter is organized as follows The second section discusses the prototype polar smectics the ferroelectric liquid crystals. We discuss the structure of the ferroelectric phase, the theoretical explanation for it and we introduce the flexoelectric effect in chiral polar smectics. Next we introduce a new set of chiral polar smectics, the antiferroelectric liquid crystals, and we describe the structures of different phases found in these systems. We present the discrete theoretical modelling approach, which experimentally consistently describes the phases and their properties. Then we introduce the discrete form of the flexoelectric effect in these systems and show that without flexoelectricity no interactions of longer range would be significant and therefore no structures with longer periods than two layers would be stable. We discuss also a few phenomena that are related to the complexity of the structures, such as the existence of a longitudinal, i.e. parallel to the... 

Antiferroelectric liquid crystals were discovered in 1989.xheir antiferroelectric properties were considered as a surprise as, at that time, nobody believed that significant changes of the tilt from layer to layer were possible. In addition to the surprising antiferroelectric properties of one of the phases, several additional phases within a rather narrow temperatm-e region were found. Why such a rich variety of phases occurs within a narrow temperature region and what their structures are, has been a hot experimental and theoretical problem for a long time. The main difference between the microscopic structm-es of the phases was the period of the basic structure. Various phases will be described in more detail later but here we only mention the periods. The SmC phase is defined by the structure of a single... 

In the previous section flexoelectric interactions were not considered in the free energy. We have also seen that only three of the structures found in antiferroelectric liquid crystals can be explained with the form of the free energy presented in the previous section. Let us first consider the discrete form of the flexoelectric effect and its influences on the theoretical description of the structures. We shall see that the flexoelectric effect is a source of indirect interactions between more distant layers and consequently the reason for all structures that cannot be expressed by the single phase difference. 

In more complex chiral polar smectics, antiferroelectric liquid crystals, there are many consequences of the flexoelectric effect. It influences interlayer interactions and causes indirect interactions between more distant layers to appear and become important. The phenomenon is the reason for the appearance of commensurate structures that extend up to six layers. In addition, longitudinal polarization, i.e. the polarization that has a component parallel to the tilt, exists in more complex structures such as the SmCpi2, the SmC jj and the SmC phases. Unfortunately it seems that flexoelectric polarization cannot be detected separately from other phenomena by simple means. A way of measuring the flexoelectric contribution in tilted polar smectics still seems to be an open question. 

The molecular interaction between each lajrer is weak and the molecular directors in one layer are not strongly bound by molecular directors in the adjacent layers. As a result, neither a ferroelectric liquid crystal state nor an antiferroelectric liquid crystal state can be realized in forming this random orientation. In the early stages, these materials were called thresholdless antiferroelectric liquid crystals (TLAF) . However, for these materials antiferroelectric order or antiferroelectricity cannot be observed. Recently, the terms frustoelectricity and frustrated electricity have been proposed [36]. These terms imply that the formation of both ferroelectricity and antiferroelectricity are prohibited and neither phase can be formed. 

The schematic sketch in Figure 8.1 shows the usual smectic-C phase in which the tilt direction is locally constant. There are phases in which the tilt direction alternates by 180° from layer to layer or shows even more complicated behaviors. These phases will be discussed in the following chapter on antiferroelectric liquid crystals. 

It seems that finally this kind of phenomenon may have been observed in liquid crystals [135]. However, in contrast to the cases of Si02 and NaC103, the helical structures are probably possible on a molecular level as well as on a supermolecular level. Thus we may expect domains of nonchiral molecules in different conformations, right and left-handed, which behave as if they belong to different enantiomeric forms. The possibility that a space-filling flexoelectric deformation will be spontaneous for certain molecular shapes and thereby create a chiral structure out of nonchiral molecules will be much enhanced if the deformation can take place in the layer rather than in the interlayer twist-bend structure of Fig. 52, and may then lead to antiferroelectric (rather than helielectric) order similar to that in antiferroelectric liquid crystals made of chiral compounds. The polarization may very... 

Otaracteristic for antiferroelectric liquid crystals are three stales of switching emerging between the zero field state with zigzag structure layer orienbtion and the two known... 

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

The flexoelectric effect is a phenomenon where a space variation of the order parameter induces polarization. Chiral polar smectics are liquid crystals formed of chiral molecules and organized in layers. All phases in tilted chiral polar smectic liquid crystals have modulated structures and they are therefore good candidates for exhibiting the flexoelectric effect. The flexoelectric effect is less pronounced in the ferroelectric SmC phase and in the antiferroelectric SmC. The flexoelectric effect is more pronounced in more complex phases the three-layer SmCpu phase, the four-layer SmCFi2 phase and the six-layer SmCe a phase. 

Since the discovery of the antiferroelectric phase, several additional chiral smectic phases have been observed, most notably the three-layer (Figure 2.17) and four-layer intermediate phases (also known as ferri-electric), SmC pn and SmC pi2. The structures of these phases are defined by repeated variations in azimuthal angle from layer to layer and have shown promise for the development of interesting new liquid crystal devices with many different switching states, but technological applications have yet to be realized. 

The banana molecules are too interesting to say now since the ferroelectric phase has been demonstrated, let s move on. Their bizarre behavior sometimes leads to ferroelectric and sometimes to antiferroelectric phases. Their optical texture is also not uniform, but they exhibit a polydomain liquid crystal phase, as if they would contain a large amount of impurities (of course the compounds were as pure as possible). The reason for this erratic behavior was proposed at a Gordon conference in 1997 the complexity of the behavior stems from the tilting of the molecules with respect to the smectic layer. Initially, we considered the molecular tilting in the B2 phase because the measured thickness of the smectic layers was far less than the calculated molecular length [131]. This fact had always been in the back of my head, but I could not find a reason why the molecular axis must tilt. 

The tilting of molecules in the B2 phase is clearly confirmed from the observation that the spherulites emerging from the isotropic phase show an electric field dependence of the position of the optical extinction lines (Fig. 9.26). Because of the tilting of banana molecules to the layer, chirality is spontaneously generated in addition to the polarity this fact sounds shocking but is so simple to be understood [132, 133]. If the molecule is rotated around their polar axis (the orientation of the bent in the molecules), which is akin to tilting the molecules in the layer, the rotation operation cannot be achieved by a simple translation (see Fig. 9.27). That is, these two states are in a mirror relation with left-handed and right-handed chirality. This is called the layer chirality. When the chirality couples with the polarity of the molecules, one would consider various smectic liquid crystal structures. There are two homochiral phases in which either (—) or (-I-) chiral molecules stack in the layers and a racemic phase in which layers are alternately stacked with layers of (—) and (-I-) chiral molecules. Each of those phases can be either ferroelectric or antiferroelectric, so that in total six different phases are present... 

The mesogens are either packed in closed cylinders that arrange in a hexagonal smectic layer (columnar hexagonal (Colh) liquid crystal phase), or they form a closed-sphere cubic (Cub) liquid crystal phase (Fig. 9.32a) [149, 150]. The Colh phase has a spontaneous polarization that is in the column axis direction and shows an antiferroelectric response. Dissipative structures appear specifically in systems without molecular asymmetry. That is, as described in Fig. 9.32b, when asymmetric molecules are packed in layers, a difference in packing density occurs in the lower and upper halves of the layer [150]. 

Liquid crystal molecules usually tilt in the same direction over the smectic layers (synclinic [212]) in the smectic C (SmC) phase. However, in one of the smectic A (SmA) phases, called de-Vries phase [213,214], molecules tilt but the tile direction is random so that the overall molecular tilt cannot be recognized optically. Frustration can be produced between aligning and random orders [215]. There is another style of tilt, in which the tilting direction is aligning in one direction in each smectic layer however, tilting direction alternates between the adjacent layers (anticlinic [212]). It has been well known that the introduction of chirality into the synclinic and anticlinic stmctures produces the ferroelectric and antiferroelectric properties, respectively. Frustration between the ferroelectric and antiferroelectric properties produces the ferroelectric structure in which the spontaneous polarization is partially canceled by the different magnitude between plus and minus polarization directions [216, 217]. The anticlinic order, NOT the antiferroelectric order, has been reported to be created by achiral systems [218, 219], indicating that the frustration between synclinic and anticlinic structures occurs, without any polar effects. The clinicity is determined by the style of the molecular order between the adjacent smectic layers, and therefore, the molecular structures at the peripheral... 

Figure 2-2 shows the situation when n is parallel to the smectic layer normal k. This is similar to the SmA phase of calamitic liquid crystals, except that now the layers are polar. This difference is designated by adding the letter P (for polar) to SmA. In this case one can have two distinct situations, the layer polarization P can be either parallel or antiparallel in the subsequent layers corresponding to ferroelectric (SmAP ) or antiferroelectric (SmAP ) subphases. Here and later... 

---